Abstract

We present a novel data structure, the Bayes tree, that provides an
algorithmic foundation enabling a better understanding of existing
graphical model inference algorithms and their connection to sparse matrix
factorization methods. Similar to a clique tree, a Bayes tree encodes a
factored probability density, but unlike the clique tree it is directed
and maps more naturally to the square root information matrix of the
simultaneous localization and mapping (SLAM) problem. In this paper, we
highlight three insights provided by our new data structure. First, the
Bayes tree provides a better understanding of batch matrix factorization
in terms of probability densities. Second, we show how the fairly abstract
updates to a matrix factorization translate to a simple editing of the
Bayes tree and its conditional densities. Third, we apply the Bayes tree
to obtain a completely novel algorithm for sparse nonlinear incremental
optimization, that combines incremental updates with fluid relinearization
of a reduced set of variables for efficiency, combined with fast
convergence to the exact solution. We also present a novel strategy for
incremental variable reordering to retain sparsity.We evaluate our
algorithm on standard datasets in both landmark and pose SLAM settings.